Learn French: Son avis est très important. - His opinion is very important.

It can mean either! In French, the possessive adjective (son, sa, ses) agrees with the noun being owned, not the owner. Since avis is masculine, we use son. This could translate to "his opinion" or "her opinion" depending on the context.

Since this lesson is about opinions and the subjunctive, does the phrase à mon avis trigger the subjunctive?

No, it triggers the indicative! The phrase à mon avis (in my opinion) introduces a statement you believe to be true. Just like an affirmative je pense que or je crois que, it is followed by the normal indicative mood.

If I change this sentence to say "It is important that he gives his opinion," do I need the subjunctive?

Yes, you do. While our example sentence states a simple fact using the indicative, the impersonal expression il est important que expresses a subjective necessity or value judgment. This means the verb that follows must be in the subjunctive, like this: Il est important qu'il donne son avis.

What is the difference between un avis and une opinion?

They are very similar and often interchangeable, but un avis is typically used for a specific view, judgment, or piece of advice on a particular matter, while une opinion often refers to a broader personal belief or worldview.